journal of the mechanical behavior of biomedical materials 39 (2014) 257–269

Available online at www.sciencedirect.com

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Research Paper

Soft material adhesion characterization for in vivo locomotion of robotic capsule endoscopes: Experimental and modeling results Madalyn D. Kerna,n, Joan Ortega Alcaidea,b, Mark E. Rentschlera a

University of Colorado at Boulder, 427 UCB, 1111 Engineering Dr., Boulder, CO 80309-0427, USA Polytechnic University of Catalonia, Diagonal Avenue, 647, 08034 Barcelona, Spain

b

art i cle i nfo

ab st rac t

Article history:

The objective of this work is to validate an experimental method and nondimensional

Received 25 April 2014

model for characterizing the normal adhesive response between a polyvinyl chloride based

Received in revised form

synthetic biological tissue substrate and a flat, cylindrical probe with a smooth poly-

15 July 2014

dimethylsiloxane (PDMS) surface. The adhesion response is a critical mobility design

Accepted 21 July 2014

parameter of a Robotic Capsule Endoscope (RCE) using PDMS treads to provide mobility to

Available online 7 August 2014

travel through the gastrointestinal tract for diagnostic purposes. Three RCE design

Keywords:

characteristics were chosen as input parameters for the normal adhesion testing: pre-

Normal adhesion

load, dwell time and separation rate. These parameters relate to the RCE's cross sectional

Soft material

dimension, tread length, and tread speed, respectively. An inscribed central composite

In vivo

design (CCD) prescribed 34 different parameter configurations to be tested. The experi-

Robotic locomotion

mental adhesion response curves were nondimensionalized by the maximum stress and total displacement values for each test configuration and a mean nondimensional curve was defined with a maximum relative error of 5.6%. A mathematical model describing the adhesion behavior as a function of the maximum stress and total displacement was developed and verified. A nonlinear regression analysis was done on the maximum stress and total displacement parameters and equations were defined as a function of the RCE design parameters. The nondimensional adhesion model is able to predict the adhesion curve response of any test configuration with a mean R2 value of 0.995. Eight additional CCD studies were performed to obtain a qualitative understanding of the impact of tread contact area and synthetic material substrate stiffness on the adhesion response. These results suggest that the nondimensionalization technique for analyzing the adhesion data is sufficient for all values of probe radius and substrate stiffness within the bounds tested. This method can now be used for RCE tread design optimization given a set of environmental conditions for device operation. & 2014 Elsevier Ltd. All rights reserved.

n

Corresponding author. Tel.: þ1 720 560 3362. E-mail addresses: [email protected] (M.D. Kern), [email protected] (J. Ortega Alcaide), [email protected] (M.E. Rentschler). URL: http://www.colorado.edu/mechanical/amtl/ (M.E. Rentschler). http://dx.doi.org/10.1016/j.jmbbm.2014.07.032 1751-6161/& 2014 Elsevier Ltd. All rights reserved.

258

1.

journal of the mechanical behavior of biomedical materials 39 (2014) 257 –269

Introduction

There are several diseases that affect the gastrointestinal (GI) tract. These diseases typically fall into two general categories: diseases due to inflammation and diseases due to the abnormal growth of cancerous cells. Inflammatory bowel disease (IBD) including Crohn's disease and Ulcerative Colitis are examples of diseases caused by inflammation in the bowel. These diseases have a high incidence rate in the United States and other select regions of the world (Horsthuis et al., 2008). Currently, there are no cures for these diseases; however, if diagnosed correctly, these diseases can be managed through a variety of treatments (D'Haens et al. 2011,). Colorectal cancer (CRC) remains among the top five most common types of cancer for both men and women in the United States (Siegel et al., 2014). Jemal et al. (2010) reported that CRC incidence rates have declined in regions of historic high incidence rate, such as the United States, but that they have also increased in regions of historic low incidence rate, such as Japan. Additionally, if diagnosed with any form of IBD, the risk of developing Colorectal Cancer can increase by 0.5–1.0% (Munkholm, 2003). The most reliable and used diagnostic procedure for GI diseases is endoscopy. An upper endoscopy allows clinicians to view a patient's upper GI tract including the esophagus, stomach and the most proximal section of the small bowel, the duodenum. A colonoscopy is performed in order to view regions of the large bowel, including the rectum and colon. The device currently used for these procedures is an endoscope. Endoscopes are composed of three main sections: the control section, the insertion tube and the connector section (Varadarajulu et al., 2011). The control section houses the main electronics of the device including imaging, scope tip articulation, insufflation and suction controls. Additionally, the entry port for accessory instruments is found in the control section. The insertion tube is a long, flexible probe with a camera and light source at the tip and open channels that run the length of the scope to guide accessory instruments through the insertion tube. Finally, the connector section is the portion of the endoscope that attaches to external imaging, light, carbon dioxide and electrical sources. The working length of endoscopes varies from 925 mm to 1700 mm depending on the region of the GI tract the clinician is hoping to view (Varadarajulu et al., 2011). In some cases, an alternate method of endoscopy is used. The PillCams is a commercially available capsule endoscope that a patient swallows. As it moves passively through the GI tract it takes images ranging from 2 to 35 fps depending on location and travel speed, and sends them to an external recorder for the clinicians to view at a later time (Given Imaging, 2014). While this device allows the entire GI tract to be imaged, there is no control of the device while it is inside the patient. The images can be disorienting for clinicians and the device may not capture images at specific regions of interest. Additionally, a study of 22,840 procedures using small bowel capsule endoscopes reported an overall pooled retention rate of 1.6% (Liao et al., 2010). In order to overcome some of the shortcomings of traditional and capsule endoscopy, several research groups have worked to develop other endoscopic devices. In order to gain more control of the tip of the endoscope, Long et al. (2006)

developed the CathCam which is a catheter-based endoscope with guide wire to control the scope tip. The Aer-O-scope, developed by Vucelic et al. (2006), was developed to provide a skill independent, self-propelling, self-navigating endoscope in order to reduce the amount of training and skill required by the clinician to perform an endoscopic procedure. Other groups have focused on mobility methods for active robotic capsule endoscopes. Inchworm locomotion was presented by Cosentino et al. (2009) with the Endotics System, external magnet propulsion was presented by Valdastri et al. (2011) for actuating miniature swimming robots and spiral shaped endoscope bodies were presented by Cosentino et al. (2009), Valdastri et al. (2011), and Sendoh et al. (2003). Our group has focused on the use of micropatterned polydimethylsiloxane (PDMS) treads for mobility. Sliker et al. (2012) presented an active robotic capsule endoscope (RCE) prototype tested in vivo which used the micropatterned PDMS treads on all sides of the capsule to move through the colon (Fig. 1). The micropatterned treads were inspired by work done by Karagozler et al. (2006). While our group has demonstrated the feasibility of PDMS micropatterned treads for mobility in the large bowel (Sliker et al., 2012), it is important to characterize the treads with respect to mobility so they can be optimized for performance. Sliker and Rentschler (2012) and Sliker et al. (in press) have developed an automated traction measurement device in order to measure the traction force that the micropatterned PDMS treads provide when moving across a synthetic biological tissue substrate. Traction force was measured while varying the translational speed of the treads, the normal force between the treads and the substrate, the slip ratio (a ratio between the translational and rotational speed of the treads) and substrate hydration. Additionally, Terry et al. (2012a) has presented preliminary work describing adhesive tack and peel strengths between the porcine mucosal tissue and engineering materials, such as PDMS, stainless steel and polycarbonate. The results of the work by Terry et al. (2012a) suggest that the adhesive tack strength between the mucosa and all engineering materials is significantly larger than the peel strength. Additionally, an increasing trend of the tack and peel strengths was observed between the various materials tested

3 mm

Robotic Capsule Endoscope 37.5 mm

Quarter

Camera

PDMS Treads

LEDs 28.6 mm

Fig. 1 – Robotic Capsule Endoscope (RCE) using micropatterned PDMS treads for mobility.

journal of the mechanical behavior of biomedical materials 39 (2014) 257 –269

(i.e., the tack and peel strength of the stainless steel was less than those of the polycarbonate which was less than those of the PDMS) (Terry et al., 2012a). Further, an approximate proportional relationship was observed between the tack and peel strengths of the same type material – all peel strength values for the stainless steel, polycarbonate and PDMS materials were approximately 3.5 times smaller than the respective adhesive tack strengths. The work presented in this paper builds upon the adhesion testing methods presented by Terry et al. (2012a) and focuses on a normal dry adhesion response between a smooth PDMS layer and polyvinyl chloride (PVC) based synthetic biological tissue substrate. While the dry adhesion testing environment is not fully representative of an in vivo bowel environment, characterizing the dry adhesion characteristics is a necessary first step. The authors also acknowledge that due to the design of the RCE treads (Fig. 1) the primary adhesion modality that the RCE experiences while traveling is adhesion from peeling rather than a normal separation. However, due to the approximate proportional relationship between the tack and peel strengths observed in Terry et al. (2012a) and the fact that conducting repeatable and reliable experimental peel tests with soft materials can be challenging due to several procedural requirements including pre-load, the authors are confident that characterizing the normal adhesion between the synthetic biological tissue and smooth PDMS layer is useful and can be scaled to estimate a peeling response if desired. A unique adhesion model directly related to critical design parameters of the RCE (Fig. 1) is presented in this work as well as a characterization of critical adhesion response parameters, including maximum stress (σmax), defined as the ratio of the maximum measured force and the total probe contact area, total vertical probe displacement (δtotal) during the adhesion response and total effective adhesion energy (Eeff), defined as the total area under the force displacement curve in the tensile region. These values are critical to know when designing an RCE in order to minimize any tissue damage or other adverse effects, inhibiting the performance of the RCE. A smooth PDMS layer was used in order to obtain a fundamental understanding of the adhesion response of PDMS on the synthetic biological tissue and to have a control configuration to compare adhesion results of future PDMS tread configurations. The use of the PVC based synthetic biological tissue is well characterized and justified in Section 2.3. The normal adhesion between the PDMS treads and the inner lumen of the bowel will likely influence the translational traction of the RCE. Thus, the methods and preliminary results from this study are imperative and can be used in future work for developing an RCE mobility model.

2.

Materials and methods

2.1.

Adhesion tack test

An adhesion tack test was designed to test the normal dry adhesion response between a PVC based synthetic biological tissue of finite thickness and a flat probe with a smooth PDMS layer (Fig. 2). An MTS InsightTM II Material Testing System

259

5 N Load Cell

Acrylic Probe

Smooth PDMS Layer

Synthetic Biological Tissue

Base Platform

Fig. 2 – An MTS material testing system was used for the adhesion tack test experiments. An acrylic base platform was fixed to the MTS and a synthetic tissue sample of finite thickness was placed on top of a piece of sandpaper attached to the platform to ensure no slip conditions. A cylindrical probe made of acrylic with a smooth PDMS layer on the bottom was coupled to a 5 N load cell. The load cell and probe were attached to the MTS crosshead and were restricted to moving in the vertical direction.

(MTS Systems Corporation, Eden Prarie, MN) was used to press a flat, cylindrical probe into the synthetic tissue substrate to achieve a specified pre-load (Fpre), held for a specified dwell time (tdwell) and then separated at a specified separation rate (vsep). A 5 N load cell was used to monitor the force over time and a proportional-integral-derivative (PID) controller within the MTS Software was used to control the position of the MTS crosshead over time. A 90 s wait time was observed between test runs. The three input parameters, pre-load, dwell time and separation rate were chosen to reflect critical RCE design parameters. The small bowel is a tubular organ connecting the stomach and the large bowel. The nutrients from ingested food are absorbed and deposited into the circulatory system as food moves through the small bowel. A complex series of forces, called the migrating motor complex (MMC) (Terry et al., 2012b), is the mechanism which assists in the absorption and advancement of food or any solid bolus through the small bowel. A component of the MMC is the myenteric contact force, a normal force between the inner lumen of the small bowel and a solid bolus inside the small bowel. Terry et al. (2012b) report that the bowel exerts a mean myenteric contact load of 1.04 N/cm in the radial direction measured with a custom built myenteric force sensor (MFS). This contact force is a critical RCE design parameter as the RCE will be required to overcome this contractile force in order to actively move through the bowel. The authors

260

journal of the mechanical behavior of biomedical materials 39 (2014) 257 –269

recognize that the myenteric contact load likely changes with an increased or decreased device diameter. The cross sectional dimension in the RCE in Fig. 1 is about 29 mm and the MFS has a diameter of about 22 mm. Therefore, rather than using the contact area measurements from the RCE, a characteristic pressure was calculated using the contact area measurements of the MFS assuming that new generations of the active RCE will be smaller in size in order to operate in the small bowel. The characteristic pressure was calculated by multiplying the distributed load by the length of the MFS and then dividing that quantity by the MFS contact area. This characteristic pressure was approximately 3.0 kPa and was converted to a point load by multiplying the tack test probe area by the characteristic pressure. This load (2.5 N) was used as a pre-load in the adhesion tack test. Two additional preload values, one higher value and one lower value, were also chosen to test in order to determine how changing the RCE's cross sectional diameter affects the adhesion response. The additional pre-load values (1.0 N and 4.0 N) were chosen such that they remained within reasonable limits of the capacity of the 5 N load cell. The second adhesion test input parameter is dwell time. Again, a characteristic dwell time was calculated to reflect the RCE design in Fig. 1. The characteristic dwell time (15 s) is equal to the product of the RCE speed and tread length, in other words, the amount of time any one point of the tread remains in contact with the bowel tissue during the RCE's constant travel. To test a range of dwell times, two additional dwell times were chosen, one higher and one lower than the characteristic dwell time by a factor of two (7.5 s and 30 s). The different dwell times are indicative of an RCE capable of moving at different speeds or having different length treads than those in Fig. 1. The third adhesion test input parameter is separation rate. This parameter is equal to the RCE's speed during travel. The RCE's (Fig. 1) speed (2.5 mm/s) was chosen as the characteristic speed and values lower and higher by a factor of two (1.25 mm/s and 5 mm/s) were also chosen to represent RCEs of slower and faster speeds. All input adhesion tack test parameters are listed in Table 1.

2.2.

Cylindrical probe

An acrylic rod was turned down to 2.8 cm (1.4 cm radius) and machined to interface with the MTS testing platform. A smooth layer of PDMS was adhered to the end of the probe as the contacting surface. The PDMS material is a Sylgards

184 Silicone Elastomer (Dow Corning Corporation, Midland, MI). The PDMS base and curing agents were vigorously mixed at a 10:1 (base:curing agent) weight ratio, yielding a 4.5 ml volume. The mixture was poured onto a 7.62 cm diameter, smooth silicon wafer in order to make a smooth layer of PDMS 1 mm in height. The silicon wafer, with PDMS, was placed on a level surface in a Shel Lab vacuum-oven (Sheldon Manufacturing, Inc., Cornelius, OR) chamber. A vacuum was pulled and cycled in order to remove the air bubbles in the PDMS mixture created from the vigorous mixing. Once the air bubbles were completely removed, the PDMS was cured at 120 1C for 1 h. After curing, the PDMS was peeled off the silicon wafer. A double sided adhesive (3 M, St. Paul, MN) was added as a backing to the PDMS in order to secure the PDMS layer to the acrylic cylindrical probe. The PDMS was cleaned using isopropyl alcohol and an oxygen plasma surface cleaning procedure in order to adhere the double sided adhesive layer to the PDMS. Once the double sided adhesive layer was attached, the PDMS was adhered to the base of a cylindrical probe and cut to size.

2.3.

Synthetic biological tissue

In practice, an RCE traveling through the gastrointestinal tract will encounter several different effective tissue stiffnesses as the bowel tissue is not fixed in place and lies on top of and under many other abdominal organs, such as the liver, pancreas and kidneys. Wang et al. (2013) have conducted indentation relaxation material characterization tests on porcine liver and spleen tissue and reported modulus values for a Double Maxwell-arm Wiechert (DMW) model. An instantaneous modulus value for the liver and spleen can be calculated by adding the three modulus values from the DMW model together, resulting in an approximate instantaneous modulus of 17 kPa and 3 kPa, respectively. Johnson et al. (2013) have recently conducted stiffness measurements on excised healthy human bowel tissue using a microelastometer and reported an elastic modulus of 3 kPa. Additionally, Johnson et al. (2013) made measurements on excised human bowel tissue diagnosed with Crohn's disease and found that the bowel tissue stiffness can increase up to six fold. While the RCE treads will be in direct contact with the inner lumen of the bowel tissue, the effective stiffness the RCE encounters will vary due to the health of the tissue and the RCE's specific location. This study aims to test a range of substrate stiffnesses which will account for the variable stiffnesses the RCE may encounter (Section 2.5). Ultimately,

Table 1 – Low, middle and high adhesion tack test input parameters in coded and uncoded units. The coded units were generated for the CCD experimental design as described in Section 2.4. The middle uncoded values were calculated to reflect the current RCE design. Input parameters Pre-load (N)

Dwell time (s)

Separation rate (mm/s)

Uncoded

Coded

Uncoded

Coded

1.0 2.5 4.0

1 0 þ1

7.5 15 30

1 0 þ1

Uncoded 1.25 2.5 5

Coded 1 0 þ1

journal of the mechanical behavior of biomedical materials 39 (2014) 257 –269

1.61

261

reasonable given the approximate modulus values for human bowel and porcine liver and spleen presented previously.

1.6

2.4.

Load (N)

1.59

1.58

1.57

1.56

1.55

1.54 0

50

100

150

200

250

Time (s)

Fig. 3 – Representative force vs. time data obtained from the indentation relaxation material characterization test completed on the 21.5 mm synthetic biological tissue substrate.

the final RCE design will need to operate effectively and efficiently on a variety different substrate stiffnesses and thus should be designed to withstand the worst case scenario. In order to reduce the variability of the adhesion response across various input parameter configurations, a synthetic biological tissue was fabricated for the adhesion tack testing. The synthetic biological tissue, also used as a liver tissue phantom in Beccani et al. (2014), is made from a mixture of supper soft plastic (SSP) (MF Manufacturing, Fort Worth, TX) and plastic softener (PS) (MF Manufacturing, Fort Worth, TX), a PVC plastisol and bis(2-ethylhexyl) adipate, respectively. The plastics were mixed at a 4:1 (SSP:PS) volume ratio in a square glass dish. The mixture was stirred continuously and heated at 250 1C. Once the mixture changed from milky white to clear, the glass dish was removed from the heat and placed on a level surface to cool. The synthetic biological tissue fabricated for initial testing was measured to be 21.5 mm thick. The substrate was characterized using an indentation relaxation material characterization test with a 14 mm diameter aluminum indentation probe. As the thickness of the substrate and the probe diameter are of the same order of magnitude, a semi-infinite body cannot be assumed and therefore, all properties measured from this test are dependent on the substrate and probe geometry. A 10% strain was applied to the material and held constant for 300 s. Five trials were performed with a 60 s wait period between trials. The force vs. time data was collected (Fig. 3) and analyzed using a Double Maxwell-arm Wiechert (DMW) model taking into account the finite thickness factor as presented by Wang et al. (2013). From this analysis the long-term elastic constant and two short-term elastic constants with their respective time scale coefficients were determined (mean 7 standard deviation): E0 ¼ 24:30 kPa70:11, E1 ¼ 0:65 kPa70:07, E2 ¼ 0:29 kPa70:06, τ1 ¼ 1:84 s70:30, and τ2 ¼ 75:52 s718:12. The mean R2 value for the data compared to the DMW model was 0.984. An instantaneous modulus value was calculated and is estimated to be 25.24 kPa. This is

Central composite design

A central composite design (CCD) was used to organize and define an experimental testing protocol. A CCD is a classical statistical method used for tests which require large amounts of time or money to execute, both of which can limit or compromise the accuracy of the testing results (Box and Behnken, 1960; Hill and Hunter, 1966). Rather than testing all input test parameter permutations, the CCD defines a subset of tests that ensures statistically rich data while decreasing the number of tests required. For the adhesion tack test, an inscribed CCD experimental design was used, meaning the design space was restricted by the prescribed low and high parameter values. The reason for choosing the inscribed CCD was to eliminate risk of overloading the 5 N load cell during the pre-load and maintaining consistency in experimental design for all parameters. The adhesion tack test has three input parameters (preload, dwell time and separation rate) each with three levels. As described in Section 2.1 a value for each input parameter was calculated based on the design of the RCE in Fig. 1 and then a lower and higher value was chosen for each parameter. The CCD experimental design uses a coded unit system in order to normalize units of the input parameters. Therefore, the lowest value for each input parameter was assigned as “ 1”, the center value was assigned as “0” and the highest value was assigned as “þ1” as shown in Table 1. The CCD prescribed 34 input parameter configuration trials which were tested in a random order.

2.5.

Extended parameter adhesion tack test study

The authors were also interested in the effects on adhesion when tread area or substrate stiffness were varied. In order to measure these effects, the probe radius and substrate thickness were varied. Two additional radius probes (0.79 cm and 1.1 cm) were fabricated and assembled as described in Section 2.2. Additionally, two different stiffness synthetic biological tissue materials were fabricated in order to cover a range of tissue stiffness profiles. In order to limit sources of variability in the synthetic tissue material behavior, especially that at the contact surface, the authors chose to vary the stiffness of the synthetic biological tissue by varying the thickness rather than varying the ratio at which the constituents were added. The two additional substrate thicknesses (18.5 mm and 33.7 mm) fabricated correspond to different stiffness values, respectively (2.22 N/mm and 0.63 N/mm). The additional probe radius and effective synthetic substrate stiffness values are listed in Table 2.

3.

Theory and calculations

3.1.

Classical contact and adhesion models

Contact and adhesion mechanics have been studied and characterized in several ways. Hertz's (1896) contact theory

262

journal of the mechanical behavior of biomedical materials 39 (2014) 257 –269

Table 2 – Various probe radii and synthetic substrate stiffnesses were tested in order to determine how substrate stiffness and tread contact area affect the adhesion response. The thickness of the synthetic biological tissue substrate was varied to obtain various effective stiffness values. The corresponding substrate thicknesses are also listed. Extended adhesion tack test parameters Probe radius (cm)

Effective substrate stiffness (N/mm)

Substrate thickness (mm)

0.79 1.1 1.4

2.22 1.76 0.63

18.5 21.5 33.7

was the first theoretical model describing the contact between rigid, elastic solids. This theory describes how the indentation depth and the shape of the contact surface depend on the elastic properties of the materials in contact. However, Hertz's contact theory does not account for any attractive forces that may be observed when the two rigid, semi-infinite, elastic bodies approach each other. Johnson et al. (1971) were the first to present a model for the attractive forces observed when two rigid, semi-infinite, elastic solids were brought close together. They observed that in order to separate some materials, a positive net mechanical work had to be performed. The Johnson Kendall and Roberts (JKR) model characterizes the adhesion energy of the system as a function of the material surface energies and is derived from the Griffith equilibrium criterion for brittle fracture (Johnson et al., 1971). However, the semi-infinite body assumption for the JKR theory cannot be assumed for the proposed adhesion tack test as the substrate thickness is of similar order of magnitude as the contact radius and thus is considered a finite thickness. Additionally, due to the viscoelasticity of the synthetic biological tissue substrate, the crack tip will experience localized adhesive losses during crack propagation which will not follow brittle fracture theory (Barquins, 1992). Finally, the JKR theory breaks down when a super soft material is introduced. Style et al. (2013) argue that for super soft materials, the surface tension of the material is also a critical factor in defining the adhesion energy and should be included in the JKR theory. While the Hertz theory, JKR theory and Style's modification to the JKR theory are valid contact and adhesion models, none characterize the adhesion energy as a function of the critical RCE design parameters. Therefore, the authors designed and executed the CCD experimental design to understand and model the effects of pre-load, dwell time and separation rate on the adhesion response between a smooth PDMS surface and a synthetic biological tissue.

4.

Results

4.1.

Nondimensional model analysis

The stress vs. displacement adhesion tack test response curves for a complete CCD are shown in Fig. 4. The data showed clear groupings, identified and labeled in the figure, and suggested that the pre-load and separation rate input parameters were of great influence to the adhesion response curve. Additionally, all 34 curves had similar shapes, thus suggesting that the data could be nondimensionalized. All

data points were nondimensionalized by dividing the measured stress by the maximum stress and the measured displacement by the total displacement. As seen in Fig. 5, the 34 experimental nondimensional curves are very similar and a mean nondimensional curve was defined with a maximum error of 5.6% between the mean model curve and experimental nondimensional curves. In order to define this nondimensional adhesion response, a mathematical model describing the adhesion response was necessary. Rather than purely fitting a model curve to the mean nondimensional curve, the authors made a hypothesis that there were two distinct regions of the mean nondimensional curve: a linear region achieved during the initial separation of the cylindrical probe and the synthetic biological tissue and a region that was characteristic of the crack propagation and separation of the synthetic biological tissue with the cylindrical probe. Thus, if shown that the hypothesis was accurate, the model nondimensional curve would have some physical justification for its form. In order to confirm this hypothesis, the viscous properties of the synthetic biological tissue were analyzed and a high speed video analysis of the adhesion tack test was performed to determine where the crack initiation began.

4.1.1.

Linear region analysis

The indentation relaxation material characterization test results for the synthetic biological tissue substrate suggest that the material does exhibit viscoelastic behavior (Fig. 3). However, as shown in Fig. 4, the initial region of each of the 34 test configurations are independent of the loading rate. This clearly suggests that for the range of separation rates tested there is no viscoelastic effect in the bulk deformation of the substrate, thus a linear model applied to this region is reasonable.

4.1.2.

Crack propagation analysis

An Olympus iSpeed high speed camera (Olympus Imaging America, Inc., Center Valley, PA) was used to video the center CCD test configuration (pre-load¼2.5 N, dwell time¼ 15 sec, separation rate¼ 2.5 mm/s). The video was taken at 250 frames per second (fps). From the raw experimental data of the adhesion tack tests, the authors observed that the adhesion region of the entire test occurred in approximately 0.2 s. Therefore, a frame rate of 250 fps resulted in about 50 image frames over the course of the entire adhesion tack response. The high speed camera data was synchronized with the raw force vs. displacement data (acquisition rate 500 Hz) for the center CCD configuration in order to determine the approximate displacement at which the crack between the PDMS and synthetic substrate

journal of the mechanical behavior of biomedical materials 39 (2014) 257 –269

263

1500

Legend Fpre = 1.0 N Fpre = 1.608 N Fpre = 2.5 N Fpre = 3.392 N Fpre = 4.0 N

Stress, σ (Pa)

σmax range 1000

vsep = 1.25 mm/s vsep = 2.01 mm/s vsep = 3.125 mm/s vsep = 4.24 mm/s vsep = 5.0 mm/s

500

0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

δtotal range

Displacement, δ (mm) Fig. 4 – Experimental stress vs. displacement curves for the 34 CCD test configurations. All curves of the same color correspond to tests done with the same pre-load. Tests done at the same separation rate are called out with the red circles. σmax range and δtotal range specify the range of values of the maximum measured stress and total displacement for all 34 experimental configurations. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.) 1

4.1.3.

0.9

σ/ σmax (Pa/Pa)

0.8 0.7 0.6 0.5 0.4 0.3

Non-dimensional experimental curves, n=34 Mean curve

0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

(mm/mm) total Fig. 5 – Nondimensional experimental curves (blue) were obtained by dividing each curve by its respective maximum measured stress and total displacement. A mean nondimensional curve (red) was calculated and has a maximum relative error of 5.6% with the experimental nondimensional curves. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.) initiated. By working back in time from the first frame corresponding to no material contact to the frame where crack initiation began, the displacement at which the initial separation began was approximated. The synchronized high speed camera and force vs. displacement data are presented in Fig. 6. These results were a qualitative verification that the crack initiation began at the end of the linear region of the adhesion response curve.

Nondimensional mathematical model

Once the physical assumptions for the mean nondimensional curve were confirmed, a mathematical model was determined. A curve fit was performed on the two regions of the mean nondimensional curve independently. A linear fit was used for the first region. From the high speed video analysis discussed in Section 4.1.2, the approximate location of the transition point from the linear region of the curve to the crack propagation region was known. In an effort to achieve an accurate mathematical model, the linear region termination point (crack initiation point) for the mean nondimensional curve was determined by fitting a linear curve to the first half of the data (δ=δtotal ¼ 0:5). Then the termination point was incrementally reduced until the R2 value of the model and the mean nondimensional curve reached 0.99. The crack initiation displacement was determined to be approximately 30% of the total displacement (δcracK ¼ 0:3δtotal ). The authors verified that the point at which this occurred qualitatively agreed with the crack propagation initiation displacement determined from the high speed video analysis and used this relation between the crack initiation displacement and the total displacement for all testing configurations. The second region of the mean nondimensional curve was modeled assuming that the synthetic biological material continued to be linearly elongated, but due to the crack initiation and propagation additional physical and material behaviors were present which influenced the measured stress. A crack propagation function (Cðδ0 Þ) was determined such that when multiplied by the initial linear model, it corresponded with the shape of the data. The best model fit was a third order polynomial with an exponential term. Possible variables that could be included in the crack propagation function include a reduction of the surface contact

264

journal of the mechanical behavior of biomedical materials 39 (2014) 257 –269

Experimental Data

Video Frames

Force (N)

0.8

Video point

0.6

Probe 0.4 0.2 0

Synthetic tissue 0

0.2

0.4

0.6

0.8

Crack initiation

Displacement (mm) Force (N)

0.8

Video point

0.6

Probe

0.4 0.2 0

Synthetic tissue 0

0.2

0.4

0.6

0.8

Crack propagation

Displacement (mm) Force (N)

0.8

Video point

0.6

Probe 0.4 0.2 0

Synthetic tissue 0

0.2

0.4

0.6

Displacement (mm)

0.8

Complete separation

Fig. 6 – Experimental force vs. displacement output data (left) and the corresponding images take with an iSpeed high speed camera (right). Data acquisition rate was 100 Hz and frame rate was 250 fps which corresponds to about 50 images taken over the 0.2 s adhesion region. The displacement at which the crack initiated was determined by finding the first frame that had complete separation of the PDMS surface and synthetic substrate. Then moving backwards in time, the point at which the crack initiated was found.

area between the smooth PDMS and the synthetic biological tissue as the crack propagates and viscoelastic losses due to the high speed and large material strains at the crack tip. The authors recognize that the lack of specific physical justification for the crack propagation function is not ideal; however, it is a reasonable approximation necessary to define the overall adhesion response behavior. The R2 value for the second region of the adhesion model compared to the mean nondimensional curve is 0.99. The complete mathematical model for the nondimensional adhesion response curve is presented in Table 3.

4.2.

Adhesion tack test trends

There are three critical response variables that can be analyzed from the adhesion response data. These include the maximum stress (σmax) achieved during the adhesion response, the total vertical displacement of the probe (δtotal) during the adhesion response and the total effective adhesion energy (Eeff), defined as the total area under the force vs. displacement curve. The maximum stress value presented in this work is, in fact, an underestimation of the actual maximum stress the synthetic biological tissue experiences. The maximum stress, as defined in this work, is the ratio of the maximum measured force and the surface area of the entire probe. However, during the crack propagation region

there is a continuous decrease in the adhesion surface contact area. As it is difficult to measure the adhesion surface contact area in practice due to the complex kinematics of the crack propagation, the maximum stress presented in this work is assumed to be within reason, but recognized as an underestimation. When designing an RCE it is important to understand the response of each of these variables as the input parameters change. The maximum stress and total displacement parameters give some indication of tissue damage while the total effective adhesion energy is a measure of energy lost in the system due to adhesion. Additionally, these parameters can be a possible predictor of traction (Sliker et al., in press). Each of these variables was calculated from the experimental data and tabulated. Using Minitab 16, a statistical analysis software (Minitab Inc., State College, PA), a nonlinear regression of each variable was performed keeping in mind the clear influence of separation rate and pre-load observed in the original stress vs. displacement data in Fig. 4. The empirical equations chosen for each critical parameter were chosen such that both the R2 and lack-of-fit p-value were greater than 0.975 and 0.05, respectively. The empirical equations are listed in Table 4. A graphical analysis of the each of the critical response variables was done to confirm that no critical design input parameters were missing from the critical response variable

journal of the mechanical behavior of biomedical materials 39 (2014) 257 –269

265

Table 3 – The mean nondimensional curve was mathematically modeled. There are two sections of the nondimensional adhesion response curve, a linear region and a crack propagation region. The mathematical models, their constants and R2 values are listed. Model region

Model shape

Model constants

R2

Linear δoδcrack

σ δ ¼k σ max δtotal

k ¼2.404

0.99

Crack propagation δ Zδcrack

σ δ ¼k Cðδ0 Þ σ max δtotal where

a1 ¼  0:589, a2 ¼ 2:028, a3 ¼ 1.998, a4 ¼0.001, a5 ¼ 8.649

0.99

0

0

0

Cðδ0 Þ ¼ a1 δ0 þ a2 δ 2 þ a3 δ 3 þ a4 ð1 ea5 δ Þ δ0 ¼ δ δcrack

Table 4 – Empirical equations as a result of a non-linear regression analysis for the critical response variables. The R2 is a measure of how accurate the predicted value is when compared to the measured value, the maximum error is the largest percent error between the predicted and measured values and the lack-of-fit p-value is a measure of how well the nonlinear model fits the data. A p-value o0:05 indicates that there is reason to believe the model does not fit the data well. R2

Maximum error (%)

Lack-of-fit p-value

2 σ max ¼ 972:491v0:310 sep  7:711Fpre  9:577Fpre vsep

0.990

2.04

0.451

Total displacement

δtotal ¼ 0:791v0:300 sep

0.996

1.47

0.929

Effective adhesion energy

Eeff ¼ ð0:155vsep  0:010Fpre vsep Þ0:583

0.994

3.26

0.247

Critical design parameter

Model equation

Maximum stress

empirical equations. All the values for each critical response variable were plotted against their respective separation rate and ordered by increasing separation rate and then by increasing pre-load within the separation rate groups (Fig. 7). From these plots it is clear that the separation rate is a significant factor in all three critical parameters while pre-load only has a significant influence on the σmax and Eeff parameters. The dwell time input parameter seems to have no effect on any of the critical parameters. These dependencies are reflected in the empirical equations for the critical response variables. With the nondimensional adhesion model and the empirical equations for the critical response variables, it is possible to reconstruct a dimensionalized adhesion curve for any set of critical design input parameters. This gives some indication of how accurate the nondimensional and empirical models are for the adhesion response. For example, if the center configuration of critical design input parameters (preload¼ 2.5 N, dwell time¼15 s, separation rate¼2.5 mm/s) is chosen, the nondimensional model can be scaled back to a dimensional space by multiplying the calculated σmax and δtotal by the nondimensional model curve. The predicted and experimental curves for this configuration are presented in Fig. 8. This process was done for all experimental configurations defined by the CCD and the mean R2 value for all configurations was 0.995.

4.3.

Probe radius and substrate stiffness analysis

A full CCD analysis was completed for each of the probe radius–substrate stiffness combinations (a total of 9 probe radius–substrate stiffness configurations, Fig. 9a). Again, the stress vs. displacement data for each probe radius–substrate stiffness configuration had similar shapes and could be

nondimensionalized. The nondimensional experimental data for the nine probe radius–substrate stiffness configurations are presented in Fig. 9b. The results indicate a clear increasing relationship for all of the critical response variables with respect to separation rate. Also, as stiffness increases, the σmax increases for all probe radii, the δtotal decreases for all probe radii and the Eeff decreases for the two larger probe radii (1.4 cm and 1.1 cm). Finally, it was observed that the σmax was minimized with the largest probe radius for all substrate stiffnesses while the δtotal and Eeff were minimized with the smallest probe radius for all substrate stiffnesses.

5.

Discussion

The normal adhesion response which occurs between a smooth PDMS surface and a synthetic biological tissue substrate is important to understand when designing an RCE. The adhesion of the tissue to the treads should be minimized in order to minimize tissue damage and RCE power losses. However, the translational traction generated for mobility may require some trade off in the amount of adhesion that can be minimized (Sliker and Rentschler, 2012; Sliker et al., in press). The CCD experimental study provided useful information which can be used to characterize this adhesion response. The authors have shown that the adhesion response of a smooth PDMS surface on a synthetic biological tissue substrate can be characterized by a nondimensional model, composed of a linear region and crack propagation region. From a mathematical point of view, this nondimensionality is a simplistic approach to define the adhesion response for a variety of input parameter configurations. However, from a

266

journal of the mechanical behavior of biomedical materials 39 (2014) 257 –269

Maximum Stress as a Function of Separation Rate F

1450

F

Center Configuration Model

1200

1500 = 2.5 N

= 1.608 N

1000

1400

σmax

F

800

= 1.0 N

1300

F

1250

F

= 2.5 N

F

= 4.0 N

σ (Pa)

(Pa)

1350

= 3.392 N

1200

400

1150

F

= 1.608 N

F

= 3.392 N

1100

200

1050

0

1000 F 950

1

= 2.5 N

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Separation Rate (mm/s) Total Displacement as a Function of Separation Rate 1.3

F

= 2.5 N

1.25 F

1.2

(mm) total

F

1.1

= 1.0 N, 2.5 N, 4.0 N

1.05 1 F

= 1.608 N, 3.392 N

0.95 0.9 F

0.85 1

= 2.5 N

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Separation Rate (mm/s)

Total Effective Adhesion Energy As a Function of Separation Rate 0.8 F

0.75

= 2.5 N F

= 1.608 N

F

= 3.392 N

0.7 0.65 0.6 0.55

F F

= 1.0 N = 2.5 N

F

= 4.0 N

0.5 0.45

F

= 1.608 N

F

= 3.392 N

0.4 F

0.35 1

= 2.5 N

1.5

2

2.5

0

0.2

0.4

0.6

0.8

1

(mm)

Fig. 8 – Experimental data for center CCD configuration compared to the reconstructed model curve. This was done for all experimental configurations and the mean R2 value was 0.995.

= 1.608 N, 3.392 N

1.15

Eeff (mJ)

600

3

3.5

4

4.5

5

5.5

Separation Rate (mm/s) Fig. 7 – Experimental results for maximum stress, total displacement and total effective adhesion energy vs. adhesion test separation rate. Tests done at specified preloads are labeled.

design point of view, the specific shape of the curve may not be as important as the critical response variables unique to every input parameter configuration. The σmax, δtotal, and Eeff are critical parameters that should be considered when

designing an RCE as they will influence the performance of the RCE as it travels. Each of these parameters should be minimized in order to minimize adverse adhesion effects. The authors have presented nonlinear empirical models for each of these variables in terms of the input parameters, Fpre, tdwell and vsep. It was determined that the vsep had the most significant effect on each of the critical response parameters. This result is supported by adhesion literature. In particular, Barquins observes the increase in tack force with increased cross-head velocity when measuring the tackiness of different elastomers (Barquins, 1992; Barquins and Maugis, 1981). Barquins (1992) attributes this response to the increase in viscoelastic losses that occur at crack tip with an increase in separation rate. Since the initial region of the adhesion curve was determined to be linear and independent of loading rate, it is reasonable to assume that the synthetic substrate used in this study experiences viscoelastic losses once the crack initiates and propagates. The Fpre was only a significant factor for the σmax and Eeff while and tdwell had no observed significant effect. As the Fpre increased, both the σmax and Eeff decreased. While it was not confirmed, it is possible that the increase in Fpre disrupted the adhesion contact or caused viscoelastic losses due to the increased strains during compression. This method of minimizing the σmax and Eeff, that of increasing the Fpre, is not advised, however, in optimizing the adhesion response as it may cause tissue damage in the compression phase. While it has been reported in the literature (Barquins and Maugis, 1981) that the dwell time of an elastic adhesion contact has a positive influence on the tack strength between the elastic materials, this effect was not observed in this study. This is likely due to the fact that the substrates used in this study are viscoelastic which may cause energy losses that do not allow the trends of elastic adhesion to apply. The results of the adhesion tack tests for the various probe radius–substrate stiffness configurations suggest that given the input testing parameters are within the range presented in this study, the nondimensionalization method can be used to analyze the specific shape of the adhesion response curves

journal of the mechanical behavior of biomedical materials 39 (2014) 257 –269

Radius0.79 cm

Radius1.4 cm

Medium Stiffness

High Stiffness

Radius1.1 cm

2500 2000 1500 1000 500 0 2500 2000 1500 1000 500 0

Low Stiffness

Sigma, σ (Pa)

2500 2000 1500 1000 500 0

267

0

0.5

1

1.5

2

0

0.5

1

1.5

Displacement,

Radius 0.79 cm

2

0

0.5

1

Radius 1.1 cm

High Stiffness

0.5

Medium Stiffness

0

σ/σmax (Pa/Pa)

2

Radius 1.4 cm

1

1

0.5

0

Low Stiffness

1

0.5

0

1.5

(mm)

0

0.5

1

0

0.5

1

0

0.5

1

total (mm/mm)

Fig. 9 – The dimensional and nondimensional experimental curves for the nine different configurations of probe radius and substrate stiffness values. (a) Dimensional experimental curves varying substrate stiffness and probe radius. (b) Nondimensional experimental curves varying substrate stiffness and probe radius.

for probe radius–substrate stiffness configurations that are within the bounds tested in this study. Due to the finite thickness of the synthetic biological tissue substrate, no conclusions can be made about extending this result or the observed trends for substrate stiffnesses outside the experimental bounds. Additionally, the critical adhesion response parameters had similar trends for all probe radius–substrate stiffness configurations as observed for the initial substrate stiffness tests. Separation rate was a clear influential input

parameter for all critical response variables. The results from the various probe radii suggest that in order to minimize the σmax more tread area should be in contact with the tissue substrate. However, since the entire surface area of the probe was used to calculate the σmax rather than the actual substrate-probe contact area, this observation can be misleading. If the maximum force achieved during the adhesion test is analyzed rather than the σmax (as defined in this study), the results suggest that as the probe radius increases, the

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journal of the mechanical behavior of biomedical materials 39 (2014) 257 –269

maximum force also increases. Therefore, the tread area of the RCE will need to be carefully considered in order to minimize adverse adhesion effects, while maintaining tractive properties. Finally, as the substrate stiffness decreased, the δtotal and Eeff increased, but the σmax decreased. Therefore, as the effective stiffness that the RCE encounters decreases, the stress on the tissue will be less, but the strain that the tissue may undergo will increase. The authors aim to determine what stress and strain will cause unreasonable damage to the bowel tissue in future studies so that the RCE design can accommodate these limits. This work is a preliminary characterization of the normal adhesion response between a smooth PDMS surface and a dry, flat synthetic biological tissue substrate. While there was no direct verification of the test methods or results completed in this study, the comparison of the maximum stress values reported by Terry et al. (2012a) is of the same order of magnitude as presented in this study. Therefore, the authors are confident that the testing methods are valid for analyzing the adhesive effect of the smooth PDMS layer on the synthetic biological tissue substrate material. Future studies will begin to incorporate the more complex variables that would more accurately replicate an in vivo environment. The more complex variables such as adding a mucus layer, incorporating some topology to the synthetic biological tissue substrate and conducting tests in a physiological environment will undoubtedly have an effect on the adhesion response variables. However, the adhesion response with these complexities cannot be understood without a fundamental understanding of the simplified case. The normal adhesion tack test experimental and data analysis methods have been well developed with this work and will be used in future studies.

6.

Conclusions

The authors have presented an experimental method for measuring the normal adhesion between a smooth PDMS surface and a smooth, flat synthetic biological tissue substrate. A nondimensional model was presented for a substrate stiffness of 1.76 N/mm and probe radius of 1.4 cm. This model is composed of two sections: a linear region and a crack propagation region. Three critical response variables were also characterized as functions of the adhesion test input parameters, Fpre, tdwell and vsep. The vsep input parameter was the most influential parameter for all critical response variables, thus the RCE speed is the most important parameter to consider when trying to minimize adverse adhesion effects. When compared to the experimental data, the nondimensional model scaled back to a dimensional space with the empirical σmax and δtotal equations resulted in model curves with a mean R2 of 0.995. Similar analysis was conducted for two additional substrate stiffness and probe radius configurations. The results of these tests suggest that a nondimensional model can be determined for any probe radius–substrate stiffness configuration within the bounds tested experimentally and that vsep is, again, the most influential input parameter for each probe radius–substrate stiffness configuration.

Acknowledgements The authors would like to recognize Dr. Kurt Maute, from the Department of Aerospace Engineering Sciences at the University of Colorado Boulder, for his guidance and advice to the authors. The authors would like to recognize the National Science Foundation for funding this project through the Grant CCMI 1235532. Madalyn Kern is a Graduate Research Fellow through the NSF and Joan Alcaide Ortega was funded through the Balsell's Fellowship.

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